Question

Which of the following choices is the standard deviation of the sample shown

Answer 1

Answer:  E. square root of 2

We can write that in shorthand as sqrt(2)

sqrt(2) = 1.41421 approximately

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Explanation:

Step 1)

Add up the values to get 18+19+20+21+22 = 100

Divide by n = 5, since there are 5 items in the list. So 100/n = 100/5 = 20

The sample mean is xbar = 20

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Step 2)

Subtract the mean from each data value

• 18 - xbar = 18 - 20 = -2
• 19 - xbar = 19 - 20 = -1
• 20 - xbar = 20 - 20 = 0
• 21 - xbar = 21 - 20 = 1
• 22 - xbar = 22 - 20 = 2

The results we get are: -2, -1, 0, 1, 2

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Step 3)

Square the results from the previous step

• (-2)^2 = 4
• (-1)^2 = 1
• (0)^2 = 0
• (1)^2 = 1
• (2)^2 = 4

The results here are: 4, 1, 0, 1, 4

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Step 4)

Add up those squares from the previous step: 4+1+0+1+4 = 10

Now divide by n = 5 to get 10/n = 10/5 = 2

The result 2 represents the population variance. Applying the square root to the population variance leads to the population standard deviation. So we end up with the final answer of sqrt(2). The answer is choice E.

sqrt(2) = 1.41421 approximately

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Note: if you want the sample standard deviation, then you divide by n-1 = 5-1 = 4, but the other steps are the same as before.